Question

Determine the unit impulse response h[n] for a system in Example 3.11 specified by the equation y[n] -0.6y[n - 1] -0.16y[n - 2) = 5x[n]

Answer 1

Determine the unit impulse response hind for a system specibied by the equabio yin)-0-6 yin-1) - 0.16 yin-2) = 5 min) sop yon) - 0-6 yin-1) -0.16 yin-2) = 52n) 4ppy the Z.T with Zero Initial conditions.. (am) z ym) - 06Z (yin-0) - 0.16 ZC yan-2)) = 5 z1 + 3(n) - XZ): = 3(n) :h. n- YZ) - 0.62'yez) -0.16 z ?y(z) = 5 xcz) . ycz) (1-0-671 -0.162?) = 5X(2) 522 Yz.. X(z) 1-0.6 - 0.16 7?_062 -0.16 Yezi XZ) 52² 7-08) (2 +0-) = TF 522 H(Z) Z-08)(2+0 2). HOZ) 57 ..A + Los (Z-0. 8 2 +0.2) +02 Z-0.8 => 52 = A(Z-0.8) +B(2+0.2) Coefficient az 5- A+B - Corettilient of Censtemt 0 = -0.84 +0-2B. 4-1 B = 4

H(2): + 4 2 , Z+0.2 Z_ Z-0.8 Z +0.2 Apply Inverse ZiT z'che)) = 2 () +421(205) zcanum) = a fal<!z! Roc Z [69]* cm= 1 <1 him = -0.21m um +4 (0.8inuan) Z -a Ihm = (-012) cim+ 40.8) uan)